Claudia Castro-Castro
Math 283 Spring 2020
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Courtesy of James Stewart, Calculus: Early transcendentals, 2nd edition
Courtesy of James Stewart, Calculus: Early transcendentals, 2nd edition
Courtesy of James Stewart, Calculus: Early transcendentals, 2nd edition
Polar to rectangular \( (r,\theta)\rightarrow (x,y) \)
\[ x=r\cos \theta \\y=r\sin \theta \]
Rectangular to polar \( (x,y)\rightarrow (r,\theta) \)
\[ r^2=x^2+y^2 \\
\tan \theta = \frac{y}{x},\;\cos \theta = \frac{x}{r},\;\sin \theta = \frac{y}{r} \]
Courtesy of James Stewart, Calculus: Early transcendentals, 2nd edition
Courtesy of James Stewart, Calculus: Early transcendentals, 2nd edition
\[ \iint_R f(r,\theta)dA_{polar}=\lim_{\Delta \theta \to 0 } \lim_{\Delta r \to 0 } \sum^m_{j=1} \sum_{i=1}^n f(r_i,\theta_j)\Delta A_{ij} \]
Courtesy of James Stewart, Calculus: Early transcendentals, 2nd edition
\[ dA=rdrd\theta \]
Courtesy of James Stewart, Calculus: Early transcendentals, 2nd edition
Courtesy of James Stewart, Calculus: Early transcendentals, 2nd edition
Courtesy of James Stewart, Calculus: Early transcendentals, 2nd edition